Yes, God is free to do as He wills. However the Bible says it is impossible for God to lie. But again, He is not willing to lie, so He is perfectly free in His will to accomplish all that He wills. Whereas man's will is not free, but is in bondage to his nature, whether that be a sinful nature inherited from Adam, or a new nature given by Christ in the second birth, resulting in a faith in Christ which cannot stop believing in Him. Likewise, natural man is bound in that he cannot understand the things of the Spirit of God, for they are foolishness to him. Neither can he know them for they are spiritually discerned. Natural man is spiritually dead and therefore cannot choose Christ. This is one reason why it is a false gospel to preach that human will makes God's promises effectual.
As for the regenerated children of God, there is a conflict in them, carrying about the body of this death, the flesh lusting against the spirit and the spirit agains the flesh, so they cannot do all the things that they wish.
So, God's will is indeed free, but man's will is not. The main argument in the Bible is that man is a captive of the devil to do his will, unless/until Christ makes alive by His power, of His grace and not of man's will at all. In matters of will, this is the only relevant application to pursue. Does man have a free will to choose Christ? The Biblical answer is an emphatic No! All other talk about will is vanity.